Difference between revisions of "2018 AMC 8 Problems/Problem 7"
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<math>\textbf{(A) }1\qquad\textbf{(B) }3\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7</math> | <math>\textbf{(A) }1\qquad\textbf{(B) }3\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7</math> | ||
{{AMC8 box|year=2018|num-b=6|num-a=8}} | {{AMC8 box|year=2018|num-b=6|num-a=8}} | ||
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| + | ==Solution== | ||
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| + | We use the property that the digits of a number must sum to a multiple of <math>9</math> if it are divisible by <math>9</math>. This means <math>2+0+1+8+U</math> must be divisible by <math>9</math>. The only possible value for <math>U</math> then must be <math>7</math>. Since we are looking for the remainder when divided by <math>8</math>, we can ignore the thousands. The remainder when <math>187</math> is divided by <math>8</math> is <math>\boxed{\textbf{(B) }3}</math> | ||
Revision as of 12:22, 21 November 2018
Problem 7
The 
-digit number 
is divisible by 
. What is the remainder when this number is divided by 
?
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
Solution
We use the property that the digits of a number must sum to a multiple of if it are divisible by . This means 
must be divisible by . The only possible value for 
then must be 
. Since we are looking for the remainder when divided by , we can ignore the thousands. The remainder when 
is divided by is 
